TSTP Solution File: SET637+3 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET637+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 14:34:59 EDT 2023
% Result : Theorem 0.20s 0.58s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 58 ( 9 unt; 11 typ; 0 def)
% Number of atoms : 119 ( 16 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 125 ( 53 ~; 51 |; 12 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 8 >; 6 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 86 ( 4 sgn; 40 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
intersection: ( $i * $i ) > $i ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
intersect: ( $i * $i ) > $o ).
tff(decl_25,type,
empty_set: $i ).
tff(decl_26,type,
not_equal: ( $i * $i ) > $o ).
tff(decl_27,type,
empty: $i > $o ).
tff(decl_28,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_29,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_30,type,
esk3_1: $i > $i ).
tff(decl_31,type,
esk4_0: $i ).
tff(decl_32,type,
esk5_0: $i ).
fof(empty_defn,axiom,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_defn) ).
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(intersection_defn,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(equal_member_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(intersect_defn,axiom,
! [X1,X2] :
( intersect(X1,X2)
<=> ? [X3] :
( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
fof(prove_th119,conjecture,
! [X1,X2] :
( intersect(X1,X2)
<=> not_equal(intersection(X1,X2),empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th119) ).
fof(not_equal_defn,axiom,
! [X1,X2] :
( not_equal(X1,X2)
<=> X1 != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_equal_defn) ).
fof(c_0_7,plain,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
inference(fof_simplification,[status(thm)],[empty_defn]) ).
fof(c_0_8,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
fof(c_0_9,plain,
! [X4,X5,X6] :
( ( member(X6,X4)
| ~ member(X6,intersection(X4,X5)) )
& ( member(X6,X5)
| ~ member(X6,intersection(X4,X5)) )
& ( ~ member(X6,X4)
| ~ member(X6,X5)
| member(X6,intersection(X4,X5)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])]) ).
fof(c_0_10,plain,
! [X27,X28,X29] :
( ( ~ empty(X27)
| ~ member(X28,X27) )
& ( member(esk3_1(X29),X29)
| empty(X29) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).
fof(c_0_11,plain,
! [X13] : ~ member(X13,empty_set),
inference(variable_rename,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X14,X15,X16,X17,X18,X19] :
( ( ~ member(X16,X14)
| member(X16,X15)
| X14 != X15 )
& ( ~ member(X17,X15)
| member(X17,X14)
| X14 != X15 )
& ( ~ member(esk2_2(X18,X19),X18)
| ~ member(esk2_2(X18,X19),X19)
| X18 = X19 )
& ( member(esk2_2(X18,X19),X18)
| member(esk2_2(X18,X19),X19)
| X18 = X19 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_member_defn])])])])])]) ).
fof(c_0_13,plain,
! [X7,X8,X10,X11,X12] :
( ( member(esk1_2(X7,X8),X7)
| ~ intersect(X7,X8) )
& ( member(esk1_2(X7,X8),X8)
| ~ intersect(X7,X8) )
& ( ~ member(X12,X10)
| ~ member(X12,X11)
| intersect(X10,X11) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[intersect_defn])])])])])]) ).
cnf(c_0_14,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( member(esk3_1(X1),X1)
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,negated_conjecture,
~ ! [X1,X2] :
( intersect(X1,X2)
<=> not_equal(intersection(X1,X2),empty_set) ),
inference(assume_negation,[status(cth)],[prove_th119]) ).
cnf(c_0_17,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( member(esk2_2(X1,X2),X1)
| member(esk2_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
( intersect(X2,X3)
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( empty(intersection(X1,X2))
| member(esk3_1(intersection(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_22,negated_conjecture,
( ( ~ intersect(esk4_0,esk5_0)
| ~ not_equal(intersection(esk4_0,esk5_0),empty_set) )
& ( intersect(esk4_0,esk5_0)
| not_equal(intersection(esk4_0,esk5_0),empty_set) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
fof(c_0_23,plain,
! [X21,X22] :
( ( ~ not_equal(X21,X22)
| X21 != X22 )
& ( X21 = X22
| not_equal(X21,X22) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[not_equal_defn])]) ).
cnf(c_0_24,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_25,plain,
( empty_set = X1
| member(esk2_2(empty_set,X1),X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,plain,
( empty(intersection(X1,X2))
| intersect(X3,X2)
| ~ member(esk3_1(intersection(X1,X2)),X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,plain,
( empty(intersection(X1,X2))
| member(esk3_1(intersection(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_28,negated_conjecture,
( ~ intersect(esk4_0,esk5_0)
| ~ not_equal(intersection(esk4_0,esk5_0),empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
( X1 = X2
| not_equal(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( empty_set = X1
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,plain,
( empty(intersection(X1,X2))
| intersect(X1,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_33,negated_conjecture,
( intersection(esk4_0,esk5_0) = empty_set
| ~ intersect(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
( intersection(X1,X2) = empty_set
| intersect(X1,X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
( ~ empty(intersection(X1,X2))
| ~ member(X3,X2)
| ~ member(X3,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
intersection(esk4_0,esk5_0) = empty_set,
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,plain,
empty(empty_set),
inference(spm,[status(thm)],[c_0_17,c_0_15]) ).
cnf(c_0_38,plain,
( ~ not_equal(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_39,negated_conjecture,
( ~ member(X1,esk5_0)
| ~ member(X1,esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).
cnf(c_0_40,plain,
( member(esk1_2(X1,X2),X2)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_41,negated_conjecture,
( intersect(esk4_0,esk5_0)
| not_equal(intersection(esk4_0,esk5_0),empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_42,plain,
~ not_equal(X1,X1),
inference(er,[status(thm)],[c_0_38]) ).
cnf(c_0_43,negated_conjecture,
( ~ intersect(X1,esk5_0)
| ~ member(esk1_2(X1,esk5_0),esk4_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,plain,
( member(esk1_2(X1,X2),X1)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_45,negated_conjecture,
intersect(esk4_0,esk5_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_36]),c_0_42]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.12 % Problem : SET637+3 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n031.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 14:51:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.20/0.58 % Version : CSE_E---1.5
% 0.20/0.58 % Problem : theBenchmark.p
% 0.20/0.58 % Proof found
% 0.20/0.58 % SZS status Theorem for theBenchmark.p
% 0.20/0.58 % SZS output start Proof
% See solution above
% 0.20/0.58 % Total time : 0.017000 s
% 0.20/0.58 % SZS output end Proof
% 0.20/0.59 % Total time : 0.020000 s
%------------------------------------------------------------------------------